A priori estimates for a relativistic liquid with free surface boundary

TL;DR

This paper establishes energy estimates for a relativistic liquid with a free surface in a general Einstein spacetime, controlling key Sobolev norms of the fluid's velocity, enthalpy, and boundary geometry.

Contribution

It provides the first a priori energy estimates for relativistic free liquids with free boundaries in a curved spacetime setting.

Findings

Energy estimates control Sobolev norms of fluid velocity and enthalpy.

Estimates also control the second fundamental form on the boundary.

Results hold for small fluid velocities in Einstein spacetimes.

Abstract

We prove energy estimates for a relativistic free liquid body with sufficiently small fluid velocity in a general Einstein spacetime. These estimates control Sobolev norms of the fluid velocity and enthalpy in the interior as well as Sobolev norms of the second fundamental form on the boundary.